This function computes several statistics on a given set of labour market areas (a given partition).
StatClusterData(lma,param,threshold,dat)A list with the following components:
data.table containing the following variables for each LMA.
LMA: positive integer; labour market areas ID
EMP_live: numeric; number of commuters who live in the area
EMP_work: numeric; number of commuters working in the area
validity: numeric; validity value computed with the current parameters
EMP_live_work: numeric; number of commuters living and working in the area
lma_commuter_percent: numeric; the quantity: (EMP_live-EMP_live_work)+(EMP_work-EMP_live_work)/(2*EMP_live_work)
Home_Work_Ratio: numeric; the quantity (( EMP_live-EMP_live_work)-( EMP_work-EMP_live_work))/EMP_live_work
SC_demand_side: numeric; demand side self-containment
SC_supply_side: numeric; supply side self-containment
N_com: integer; number of communities forming the LMA
InternalCohesionLink: numeric; consistency of internal relationships. It is given by the ratio between number of links between communities inside LMA, excluding itself, and the maximum number of possible links, i.e. (N_com * (N_com-1)). See [1].
InternalCohesionFlows: numeric; intensity of internal relationships. It is the percentage of internal flows (excluding flows having as origin and destination the same node) of the LMA between different communities w.r.t the total internal flows. See [3].
NbCentralComm: integer; number of communities having a centrality index greater than 1 (for communities with more than 100 workers, the centrality index is the ratio between net incoming flows and net outgoing flows).
N_links_in: integer; number of LMAs whose residents work in the current LMA (including itself)
N_links_out: integer; number of LMAs where the residents of the current LMA work (including itself)
list containing several statistics on flows and links between the labour market areas of the given partition.
N_links: numeric; number of links between LMAs
PercNbLinksLessThreshold: numeric; percentage of links corresponding to flows below threshold
summFlows: numeric vector; summary statistics on flows
summFlowsNoItself: numeric vector; summary statistics on flows, excluding the self-flows
summLinks_in: numeric vector; summary statistics on the number of incoming flows
summLinks_out: summary statistics on the number of outgoing flows
clusterMaxNlinks_in: positive integer; the LMA ID of the cluster reaching the maximum number of incoming flows
clusterMaxNlinks_out: positive integer; the LMA ID of the cluster reaching the maximum number of outgoing flows
clusterMinNlinks_in: positive integer; the LMA ID of the cluster reaching the minimum number of incoming flows
clusterMinNlinks_out: positive integer; the LMA ID of the cluster reaching the minimum number of outgoing flows
list containing several statistics on the given partition:
NbClusters: integer; number of clusters
NbClusterUniqueCom: integer; number of clusters with an unique community
NbClustersValidLess1: integer; number of clusters with validity smaller than 1
NbClustersNoCentralCom: integer; number of clusters with no communities having a centrality measure greater than 1
Mean.SC_demand_side: numeric; mean of the demand side self-containment of the clusters in the partition
Std.SC_demand_side: numeric; standard deviation of the demand side self-containment
Mean.SC_supply_side: numeric; mean of the supply side self-containment of the clusters in the partition
Std.SC_supply_side: numeric; standard deviation of the supply side self-containment
Q1.InternalCohesionFlows: numeric; first quartile of the InternalCohesionFlows
Q2.InternalCohesionFlows: numeric; median of the InternalCohesionFlows
Q3.InternalCohesionFlows: numeric; third quartile of the InternalCohesionFlows
Q1.InternalCohesionLink: numeric; first quartile of the InternalCohesionLink
Q2.InternalCohesionLink: numeric; median of the InternalCohesionLink
Q3.InternalCohesionLink: numeric; third quartile of the InternalCohesionLink
Q1.EMP_live: numeric; first quartile of the residents
Q2.EMP_live: numeric; median of the residents
Q3.EMP_live: numeric; third quartile of the residents
Mean.EMP_live: numeric; mean value of the residents
Std.EMP_live: numeric; standard deviation of the residents
Min.EMP_live: numeric; minimum value of the residents
Max.EMP_live: numeric; maximum value of the residents
Q1.EMP_work: numeric; first quartile of the workers/jobs
Q2.EMP_work: numeric; median of the workers/jobs
Q3.EMP_work: numeric; third quartile of the workers/jobs
Mean.EMP_work: numeric; mean value of the workers
Std.EMP_work: numeric; standard deviation of the workers
Min.EMP_work: numeric; minimum value of the workers
Max.EMP_work: numeric; maximum value of the workers
Q1.EMP_live_work: numeric; first quartile of the commuters living and working in the same area
Q2.EMP_live_work: numeric; median of the commuters living and working in the same area
Q3.EMP_live_work: numeric; third quartile of the the commuters living and working in the same area
Min.EMP_live_work: numeric; minimum value of the commuters living and working in the same area
Max.EMP_live_work: numeric; maximum value of the commuters living and working in the same area
Mean.lma_commuter_percent: numeric; mean value of the quantity: (EMP_live-EMP_live_work)+(EMP_work-EMP_live_work)/(2*EMP_live_work)
Std.lma_commuter_percent: numeric; standard deviation of the quantity (EMP_live-EMP_live_work)+(EMP_work-EMP_live_work)/(2*EMP_live_work)
Mean.Home_Work_Ratio: numeric; mean value of the quantity (( EMP_live-EMP_live_work)-( EMP_work-EMP_live_work))/EMP_live_work Std.Home_Work_Ratio: numeric; standard deviation of the quantity (( EMP_live-EMP_live_work)-( EMP_work-EMP_live_work))/EMP_live_work
Q_modularity: numeric; Q_modularity index
numeric vector; it contains the parameters of the given solution, i.e. the output of the function findClusters. The parameters are minSZ,minSC,tarSZ,tarSC.
A list of data.table containing information on the labour market areas. Three components: clusterList, LWClus and marginals. clusterList is a data.table containing the variables community, cluster and EMP_live; everything else will be ignored. LWClus is a data.table containing the variables cluster_live, cluster_work and amount; everything else will be ignored. marginals is a data.table containing the variables cluster, amount_live and amount_work; everything else will be ignored.
In each data.table object, the order of the variables is mandatory.
The lma names should have not been assigned; otherwise use function DeleteLmaName.
numeric vector: the set of parameters corresponding to the lma object, i.e. minSZ,minSC,tarSZ,tarSC, respectively. See function findClusters.
numeric. It is used to identify particular small labour market areas or flows.
data frame/data.table containing the commuting flows between communities (see for example Sardinia).
Daniela Ichim, Luisa Franconi, Michele D'Alo'
[1] Erba, A., D'Angio', A. e Marzulli, S. (1990). Partizioni funzionali del territorio: il modello Isers, Franco Angeli, Milano.
[2] Franconi, L., D'Alo' M. and Ichim, D. (2016). Istat implementation of the algorithm to develop Labour Market Areas.
[3] Lipizzi, F. (2014). Strumenti e indicatori per la misura della consistenza e omogeneita' delle aree funzionali. XXXV Conferenza annuale AISRe, "Uscire dalla crisi. Citta', Comunita' e Specializzazione Intelligenti", Padova, 11-13 September 2014.
findClusters